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Evgesh-ka [11]
3 years ago
8

The circumference of a circle is 36pi cm what is the radius

Mathematics
1 answer:
alexdok [17]3 years ago
8 0

Answer:

The radius is 18 cm

Step-by-step explanation:

The formula for circumference with radius is

C = 2*pi*r

We know the circumference is 36 pi

36 pi = 2 * pi *r

Divide by pi

36 pi/pi = 2 * pi/pi *r

36 = 2r

Divide by 2

36/2 = 2r/2

18 = r

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The average American consumes 8.8 liters of alcohol per year. Does the average college student consume less alcohol per year? St
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Answer:

Null hypothesis: u = 8.8 liters

Alternative hypothesis: u < 8.8 liters

Step-by-step explanation:

The null hypothesis is always opposite to Tue alternative hypothesis and is the default hypothesis.

In this case study, the null hypothesis is that the average American consumes 8.8 liters of alcohol per year: u = 8.8

The alternative hypothesis is that does the average American consumes less than 8.8 liters of alcohol per year: u < 8.8 liters

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3 years ago
Solve the equation -4x + 7 y equals 20. Y=3x+15
satela [25.4K]

Substitue what y equals for y and solve.

-4x+7(3x+15)=20 \\-4x+27x+105=20 \\23x=-85 \\x=-\boxed{\frac{85}{23}}

Hope this helps.

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3 years ago
Find the product. (a^3b)^2 • 4ab3
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(a^3b)^2 • 4ab^3
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6 0
3 years ago
A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the stor
mixer [17]

Answer:

Critical value is t = 1.9901

Step-by-step explanation:

We are given the results of the sampling :

                                     In-House Credit Card                National Credit Card                    <u>Sample Size</u> :                              32                                                    50

<u>Mean Monthly Purchases </u>:      $45.67                                            $39.87

<u>Standard Deviation </u>:                $10.90                                             $12.47

Also, the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level α of 0.05.

<em>Firstly, we will specify our null and alternate hypothesis;</em>

Let \mu_1 = Mean Monthly Purchases of In-House Credit Card

     \mu_2 = Mean Monthly purchases of National Credit Card

So, Null Hypothesis, H_0 : \mu_1-\mu_2 = 0  {means that there is no difference in the mean monthly purchases by customers using the two types of credit cards}

Alternate Hypothesis, H_0 : \mu_1-\mu_2\neq 0  {means that there is statistical difference in the mean monthly purchases by customers using the two types of credit cards}

The test statistics that will be used here is <u>Two-sample t-test statistics</u>;

              T.S. = \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}  } }  ~ t_n___1+n_2-_2

where, \bar X_1 = Sample mean Purchases of In-House Credit Card = $45.67

           \bar X_2 = Sample mean Purchases of National Credit Card = $39.87

            s_p = pooled variance

            n_1 = In-house credit card sample = 32

            n_2 = National credit card sample = 50

So, degree of freedom of t-value here is (32 + 50 - 2) = 80

Now, at 0.05 significance level, t table gives critical value of t = 1.9901 at 80 degree of freedom.

<em>Therefore, the critical value assuming the population standard deviations are not known but that the populations are normally distributed with equal variances is t = 1.9901.</em>

4 0
3 years ago
Does the absolute value graph below flips or not flips? F(x)=2|x-9|+3
True [87]

Answer:

The absolute value graph below does not flip.

Step-by-step explanation:

New graphs are made when transformed from their parents graphs. The parent graph for an absolute value graph is f(x) = |x|.

The equation used for a new graph transformed from the parent graph is in the form f(x) = a |k(x - d)| + c.

"a" shows vertical stretch (a>1) or vertical compression (0<a<1), and <u>flip across the x-axis if "a" is negative</u>.

"k" shows horizontal stretch (0<k<1) or horizontal compression (k>1), and <u>flip across the y-axis if "k" is negative</u>.

"d" shows horizontal shifts left (positive number) or right (negative number).

"c" shows vertical shifts up (positive) or down (negative).

The function f(x)=2|x-9|+3 has these transformations from the parent graph:

a = 2; Vertical stretch by a factor of 2

k = 1; No change

d = 9; Horizontal shift right 9 units

c = 3; Vertical shift up 3 units

Since neither "a" nor "k" was negative, there were no flips, <u>also known as reflections</u>.

6 0
3 years ago
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